I'm more curious why they assumed that the prices of unhealthy foods, such as meat and dairy, won't increase too, effectively forcing people to buy and eat the healthier and still relatively cheaper plant-based food.
A couple of days ago I was travelling with a bunch of guys whom I'd have suspected of being typical Remainers (most of them typical min-age, i.e. 30-40, British guys). Since it was late and we were all hungry, we started chatting about food and health. They went on cursing the EU for, first of all, the plastic problem, then the absurd product quality requirements (no wonky vegetables and fruits, no worms and dirt on them!), GMO (not as a scientific method, but the EU control and regulations of the procedures, which are either suspiciously vague or destructive to the environment), and the general excessive bureaucracy inspired the Moloh the EU is.